1->在fragment中创建静态方法

public static void doSearch(String query){
    yourAdapter.filter(query);
}

2->从onquerytextchange方法上的活动调用此方法，并传递要搜索的查询

@Override
public boolean onCreateOptionsMenu(Menu menu) {
    getMenuInflater().inflate(R.menu.home, menu);

    MenuItem myActionMenuItem = menu.findItem(R.id.action_search);
    searchViewShop = (SearchView) myActionMenuItem.getActionView();
    searchViewShop.setOnQueryTextListener(new SearchView.OnQueryTextListener() {
        @Override
        public boolean onQueryTextSubmit(String query) {
            return true;
        }

        @Override
        public boolean onQueryTextChange(String newText) {
            YourFragment.doSearch(newText);
            return true;
        }
    });
    return true;
}

试试这个代码，
活动\u main.xml：

<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:orientation="vertical">

    <android.support.v7.widget.Toolbar
        android:id="@+id/toolbar"
        android:layout_width="match_parent"
        android:layout_height="?attr/actionBarSize"
        android:background="#009688" />

    <fragment xmlns:android="http://schemas.android.com/apk/res/android"
        xmlns:tools="http://schemas.android.com/tools"
        android:id="@+id/fragment"
        android:name="ru.lemmaproj.toolbar_search.MainActivityFragment"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        tools:layout="@layout/fragment_main" />

</LinearLayout>

fragment\u main.xml:

<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:paddingBottom="@dimen/activity_vertical_margin"
    android:paddingLeft="@dimen/activity_horizontal_margin"
    android:paddingRight="@dimen/activity_horizontal_margin"
    android:paddingTop="@dimen/activity_vertical_margin"
    tools:context=".MainActivityFragment">

    <ListView
        android:id="@+id/list"
        android:layout_width="match_parent"
        android:layout_height="wrap_content" />

</RelativeLayout>

搜索\u layout.xml：

<EditText xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    android:cursorVisible="true"
    android:imeOptions="actionDone"
    android:inputType="text" />

mainactivity.java:

public class MainActivity extends AppCompatActivity {

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        Toolbar toolbar = (Toolbar) findViewById(R.id.toolbar);
        setSupportActionBar(toolbar);
    }
}

mainactivityfragment.java:

public class MainActivityFragment extends Fragment {

    private final String[] items = new String[] { "Android", "iOS", "Windows Phone",
            "Blackberry", "WebOS", "Ubuntu", "Windows7", "Max OS X", "Linux", "OS/2" };

    private ListView listView;
    private ArrayAdapter<String> adapter;

    @Override
    public View onCreateView(LayoutInflater inflater, ViewGroup container,
                             Bundle savedInstanceState) {
        View view = inflater.inflate(R.layout.fragment_main, container, false);

        listView = (ListView) view.findViewById(R.id.list);
        adapter = new ArrayAdapter<String>(getActivity(), android.R.layout.simple_list_item_1, items);
        listView.setAdapter(adapter);

        return view;
    }

    @Override
    public void onActivityCreated(Bundle savedInstanceState) {
        super.onActivityCreated(savedInstanceState);
        setHasOptionsMenu(true);
    }

    @Override
    public void onCreateOptionsMenu(Menu menu, MenuInflater inflater) {
        super.onCreateOptionsMenu(menu, inflater);
        inflater.inflate(R.menu.menu_fragment, menu);

        MenuItem searchItem = menu.findItem(R.id.menu_search);
        SearchView searchView = (SearchView) MenuItemCompat.getActionView(searchItem);
        if (searchView != null) {
            searchView.setOnQueryTextListener(new SearchView.OnQueryTextListener() {
                @Override
                public boolean onQueryTextSubmit(String query) {
                    return true;
                }

                @Override
                public boolean onQueryTextChange(String newText) {
                    adapter.getFilter().filter(newText);
                    return true;
                }
            });
        }
    }

}

更好的方法是使用eventbus。在这样的场景中，我们必须将某些数据从一个活动传递到一个片段，这真的很有帮助。
要使用eventbus，您需要定义一个pojo类，有点像这样：

class SearchQueryEvent {
    String query;

    public SearchQueryEvent(String query) {
        this.query=query;
    }

    public String getQuery() {
        return query;
    }
}

现在，您的代码应该修改如下：
主活动.java

SearchView searchView;
@Override
public boolean onCreateOptionsMenu(Menu menu) {
    getMenuInflater().inflate( R.menu.main, menu);

    MenuItem myActionMenuItem = menu.findItem( R.id.action_search);
    searchView = (SearchView) myActionMenuItem.getActionView();
    searchView.setOnQueryTextListener(new SearchView.OnQueryTextListener() {
        @Override
        public boolean onQueryTextSubmit(String query) {
            return false;
        }
        @Override
        public boolean onQueryTextChange(String s) {
            EventBus.getDefault().post(new SearchQueryEvent(s));
            return false;
        }
    });
    return true;

}

yourfragment.java文件

@Override
public void onResume() {
    super.onResume();
    EventBus.getDefault().register(this);
}

@Override
public void onPause() {
    EventBus.getDefault().unregister(this);
    super.onPause();
}

@Subscribe(threadMode = ThreadMode.MAIN)
public void onSearchQuery(SearchQueryEvent event) {
    String query=event.getQuery();
    adapter.getFilter().filter(query);
}